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A study on conserving invariants of the Vlasov equation in semi-Lagrangian computer simulations

Part of: PLA The Vlasov Equation

Published online by Cambridge University Press:  23 March 2017

L. Einkemmer Open the ORCID record for L. Einkemmer [Opens in a new window]
L. Einkemmer*
Affiliation:
University of Innsbruck, Innsbruck, Austria
*
†Email address for correspondence: lukas.einkemmer@uibk.ac.at
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Abstract

The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov–Poisson equation. Since these methods are conservative, local in space and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes. In this paper we study the conservation of important physical invariants and the long-time behaviour of the semi-Lagrangian discontinuous Galerkin method. To that end we conduct a theoretical analysis and perform a number of numerical simulations. In particular, we find that the entropy is non-decreasing for the discontinuous Galerkin scheme, while unphysical oscillations in the entropy are observed for the traditional method based on cubic spline interpolation.

Keywords

plasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 2 , April 2017 , 705830203
Copyright
© Cambridge University Press 2017 

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